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Algorithmic market making for options

Bastien Baldacci, Philippe Bergault and Olivier Guéant
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Bastien Baldacci: CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique
Philippe Bergault: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Olivier Guéant: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an option market maker is in fact tractable. More precisely, when volatility is modeled using a classical stochastic volatility model—e.g. the Heston model—the problem faced by an option market maker is characterized by a low-dimensional functional equation that can be solved numerically using a Euler scheme along with interpolation techniques, even for large portfolios. In order to illustrate our findings, numerical examples are provided.

Keywords: Market making; Algorithmic trading; Options; Stochastic optimal control (search for similar items in EconPapers)
Date: 2021-01-02
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-03252585
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Published in Quantitative Finance, Taylor & Francis (Routledge), 2021, 21 (1), pp.85-97. ⟨10.1080/14697688.2020.1766099⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-03252585

DOI: 10.1080/14697688.2020.1766099

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